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Signatures, Heegaard Floer correction terms and quasi–alternating links


Authors: Paolo Lisca and Brendan Owens
Journal: Proc. Amer. Math. Soc. 143 (2015), 907-914
MSC (2010): Primary 57M25, 57M27; Secondary 57Q60
DOI: https://doi.org/10.1090/S0002-9939-2014-12265-9
Published electronically: October 17, 2014
MathSciNet review: 3283677
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Abstract | References | Similar Articles | Additional Information

Abstract: Turaev showed that there is a well–defined map assigning to an oriented link $L$ in the three–sphere a Spin structure $\mathbf {t}_0$ on $\Sigma (L)$, the two–fold cover of $S^3$ branched along $L$. We prove, generalizing results of Manolescu–Owens and Donald–Owens, that for an oriented quasi–alternating link $L$ the signature of $L$ equals minus four times the Heegaard Floer correction term of $(\Sigma (L), \mathbf {t}_0)$.


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Additional Information

Paolo Lisca
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

Brendan Owens
Affiliation: Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW, United Kingdom
Email: b.owens@maths.gla.ac.uk

Received by editor(s): March 7, 2013
Received by editor(s) in revised form: May 20, 2013
Published electronically: October 17, 2014
Additional Notes: The present work is part of the first author’s activities within CAST, a Research Network Program of the European Science Foundation, and the PRIN–MIUR research project 2010–2011 “Varietà reali e complesse: geometria, topologia e analisi armonica”.
The second author was supported in part by EPSRC grant EP/I033754/1.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.